Digital data is often converted into approximated gradational or gray-scale data in order to output the data through an output device such as a printer. The approximation is necessary because the output devices generally have a smaller range of output values than that of the original digital data. For example, the most printers have a predetermined number of printing elements each of which is either turned on or off to generate a dot image on an image-carrying medium. Most printers combine these elements into a unit and selectively activate a pattern of the elements in order to generate a plurality of gradational levels or multiple intensities. In other words, the increased intensity level is traded off at the cost of resolution. Despite multiple intensity levels, gradational images are often grainy.
In order to generate a visually pleasing gradational image, error diffusion techniques are used to improve the approximated intensity level. In general, error diffusion techniques distribute a difference between an approximated gradational value and an original value among the neighboring image data so as to smooth out the output image. Because of the predetermined manner of distributing the error value, the error diffusion techniques also introduce texture or visual artifacts to the output image. To avoid texture in error diffusing, during the process of approximating output values, threshold values for determining the approximated output values are varied. For example, Japanese Patent Laid Publication 62-239666 discloses a binary processing apparatus which performs error diffusion and quantization based upon a selected value from a threshold value table for reducing texture. The same reference also discloses a binary processing apparatus which performs error diffusion and adds a value stored in a table prior to quantization for reducing texture in an output image. Similarly, Japanese Patent Laid Publication 63-288755 discloses an image processing method of substantially reducing the undesirable texture in an output image. Japanese Patent Laid Publication 63-204375 also discloses a method of generating an intermediate gradational image.
The above three prior art techniques are directed to binary data and commonly employ a value table which contains periodically changing values. Although the values help generate predetermined desirable patterns in an output gradational image, undesirable texture is not sufficiently reduced by the use of the periodically changing threshold value table.
Furthermore, the gradation threshold values do not control the orientation of the desirable patterns in the output image. Even though the patterns are promoted in the output image, if the orientation of the patterns are affected by the printing process, the printed patterns are not effectively enhancing the quality of the output image. For example, the patterns are often adversely affected by jitter caused by mechanical parts for moving an image-carrying medium in a predetermined sub-scanning direction. Because of the jitter, the patterns become discontinuous or distorted, and the adversely affected patterns not only fail to enhance the visual quality of the output image, but also negatively impact the appearance of the output image.
Lastly, the above prior art techniques are not applicable to a system whose output elements are capable of generating three or more output intensity levels. In other words, output elements of certain output devices generate intermediate intensity levels other than on or off. In the multiple valued output system, a number of threshold values for each output element also correspondingly increases.